Find the remainder when x100 is divided by (x+1)3.
Solution — click to reveal
We can write x100=[(x+1)−1]100=(x+1)100−(1100)(x+1)99+(2100)(x+1)98+⋯−(97100)(x+1)3+(98100)(x+1)2−(99100)(x+1)+1.When this is divided by (x+1)3, the remainder is then (98100)(x+1)2−(99100)(x+1)+1=4950x2+9800x+4851.